I guess that really depends on what exactly you struggle with in her other relationships. Is it the fact that she's having other relationships, or is it that you don't think the guys she's dating are right for her? If it's simply that she's dating other men, then you may want to have a long hard think about whether a polyship is the right thing for you.
If you have specific concerns about specific men than that's more of a situation where you have a right to share your thoughts and feelings about the person she's dating. You can't control what she does or who she dates, but you have a right to tell her how you feel if she's dating people you think aren't good for her emotional well being. Your feelings are valid, and fair.
Personally I think if you're still struggling with her dating a particular guy after 20 months that that's ok, but if you're still struggling with the idea of her dating other men after 20 months and don't want any part of a poly relationship then you've got to really figure out what's right for you. It's ok not to feel like you can be in a poly relationship, you've given it a good try, and if it's not right for you, it's not right for you. If you feel like you can be ok with it but you need more time and patience and she's pressuring you for a timetable then you need to explain to her what you need in order to feel ok about her dating a particular person.
In my experience it's never been easy, smooth sailing all the time, there are times that really suck, and times where you feel jealous, and hurt, and like you're not being heard or listened to. In those times you need to tell your girlfriend how you feel, and it helps if you can think of ways to help alleviate those feelings. If your girlfriend wants to continue her relationship with you, then she needs to respect that you can't be ok with everything all the time. At the same time, you have to communicate to her the things that she can do to help you feel better about it. You can't control her every move, but you can explain why you have the feelings you do and suggest ways in which she can help you feel more secure in your relationship with her, within reason. What do you feel like you need in order to feel good about the relationship she's having right now?
This post I've written kind of feels rambling, but in my experience open communication and some compromises, within reason, always help tremendously. When communication breaks down and there is no give and take, then things go sideways.
You said she shuts you down when you try to suggest ways she can help you feel better about the relationship? Can you say what those suggestions are? It's tough to know what's reasonable and what's not because everyone is different, but it might help knowing what you are asking of her.